The ITV breakfast show, which replaced GMTV in September 2010, is currently fronted by Kate Garraway and Dan Lobb.
Adrian Chiles and Christine Bleakley were the franchise's first presenters, but were dropped towards the end of last year.
Kelly, who was first linked to the hosting role in March, said: "I'm really looking forward to this challenge and to working with Aled who is a warm, funny and a thoroughly decent bloke and is already a good friend."
Meanwhile, Jones added: "I am so thrilled to be joining ITV for their breakfast show. I am thoroughly looking forward to sharing the sofa every morning with such a consummate professional as Lorraine Kelly.
"We've known each other for a very long time and have always had a lot of fun together. We hope that the viewers enjoy being part of our breakfast family."
The news appears to rule out Daybreak changing its name completely due to low ratings, as had previously been speculated.
Breakfast TV favourite Kelly hosts Lorraine after the Daybreak junction between 8.30am and 9.25am, while Jones is best known for fronting BBC One's Songs of Praise.
ITV's factual and daytime commissioner, Katy Thorogood, expects the pair to become a "formidable partnership".
Both stars will take up their positions on the programme later this year.